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The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$
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$\frac{1}{2\sec\left(x\right)}\frac{d}{dx}\left(2\sec\left(x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of ln(2sec(x)). The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Taking the derivative of secant function: \frac{d}{dx}\left(\sec(x)\right)=\sec(x)\cdot\tan(x)\cdot D_x(x). The derivative of the linear function is equal to 1.